Please help with physics

Question

A 15 kg block is moving at 20 m/s along a flat surface. The coefficient of kinetic friction is 0.20. The block is 20 meters away from a horizontal spring that has a constant of 2000 N/m. How far will the spring compress to stop the block from moving?

Answer 1

First let us think about all of the equations we have to use:

 

W = - (1/2)kx² (kinetic energy for the spring, k = spring constant)

F = u_kN (coefficient of kinetic friction equation, N = normal force = mass x gravity)

W = F•d

W = ΔKE (this is an often forgotten but very important equation for solving this problem)

KE = (1/2) mv²

 

We can figure these equations out by thinking about the variables we are given and in what equations that they appear in that we know of.  I see no acceleration given in this equation, so I know that we must calculate a change in energy rather than change in force.

 

1.  First, find the initial kinetic energy.  (0.5)(15 kg)(20 m/s)² = initial KE

2. Next, we need to factor in how friction will reduce our kinetic energy before contacting the spring.

 

    F = (0.2)(15 kg)(9.8 m/s²) --->  We can calculate how much energy we lose from friction over the 20 m

    W = Fcalculated x d = F (20m)

 

3.**KEY STEP: CONVERT WORK LOST TO KINETIC ENERGY LOST.  W_{lost to friction} = 1/2mv².  solve this equation for v to get your velocity right before impact with the spring.

 

4. Final step:  Use this KE from the moment of contact with the spring to find how far the spring compresses

  KE_{before impact} = (1/2)kx². SOLVE FOR X to get answer.

 

I hope this helps!